“Pull, pull, pull!” Basil Twist called out the other day as two puppeteers struggled to drag a waterlogged blue curtain out of a five-foot-deep tank filled with 1,000 gallons of water. The tank sat in a bunkerlike room near Canal Street and Sixth Avenue. The room’s owner, Trinity Real Estate, had lent it to Mr. Twist so he could rehearse his musical puppet-reverie “Symphonie Fantastique.” Now 20 years old, the show returns to the HERE theater, just a few blocks away, for a 12-week run on Thursday.

Behind the tank, water splashed everywhere. (Mr. Twist estimates that he loses about 100 gallons per run-through.) A kind of scaffolding had been constructed around the tank, a miniature staging area. Puppeteers in wetsuits straddled the sides or scrambled into harnesses so that they could dangle above it, holding wires attached to fabric, feathers, tinsel, pinwheels. They lowered these into the water below at designated points in the music, Hector Berlioz’s “Symphonie Fantastique.”

“Every puppet show with Basil, there’s a choreography going on backstage,” said Lake Simons, a longtime Twist puppeteer. “It takes a lot to create those amazing stage pictures.” On the other side of the tank, those stage pictures were as peaceful as could be. Fringe unfurled luxuriantly, like ink spreading through a current. Bubbles ascended, echoing upward-traveling phrases in the music. Tinsel eels swam from left to right, then right to left. Pinwheels spun, shapes coalesced or flew apart.

Everything moved in sync with the music’s highs and lows, reflecting its changing themes. “I guess I’m more musical than the average Joe,” Mr. Twist, 48, said modestly. His “Symphonie Fantastique” is reminiscent of the “music visualizations” by dance pioneers like Loie Fuller, who used light and fabric to mimic the aural experience of listening to music. This may sound a bit hokey, but like great dance, Basil Twist’s musical puppetry blurs the line between the eye and the ear; the dancing feathers intensify the experience of Berlioz’s score and vice versa.

It helps that Mr. Twist’s idea of puppetry is expansive; it includes anything that can be manipulated. The puppets don’t have to look like an animal or a person or anything else. “Puppetry is an abstraction of the spark of life,” he said. In this case, “It’s just a piece of fabric, and because it’s in the water and because someone with skill is giving little impulses to it and we’re all looking at it, it looks like it’s alive.”

Over lunch, Mr. Twist recounted how he came up with the inspiration for “Symphonie Fantastique” some 20 years ago. One day, he found a small cracked aquarium lying on the sidewalk in the West Village, discarded by its owner, and dragged it home. After patching it up, he filled it with water and started experimenting: “I would take a hanger and attach a piece of fabric to it, and I could just watch it forever. It was hypnotizing.” He did this with feathers, and shapes he cut out of plastic, and fringe and anything else that came to hand. Then he experimented with light.

To this aquatic ballet, he added Berlioz’s “Symphonie Fantastique,” which he remembered from his parents’ record collection. The 50-minute piece was a respectable length, and intensely theatrical. Berlioz conceived it in 1830, after falling almost dementedly in love — from afar — with an Irish actress he saw in a performance of “Hamlet” at the Odéon theater in Paris. He poured his unrequited passion into the music, for which he wrote a loopy program note explaining its content.

His libretto lays out the story of a young musician haunted by the image of an idealized woman he sees everywhere. The protagonist, who sounds suspiciously like Berlioz, eventually smokes opium and lapses into a crazed dream, evoked by spooky bell-like sound effects and terrifying glissandi. (Berlioz too is said to have had an affection for opium.) Leonard Bernstein referred to it in his “Young People’s Concerts” as “the first psychedelic symphony in history.”

When Mr. Twist first conceived “Symphonie,” he used a recording, but now the music is played live in a transcription for solo piano written by the great Romantic-era showboat Franz Liszt. It’s a monster of a piece, which, as played by the pianist Christopher O’Riley, adds a new level of theatricality to the visual spectacle. In Mr. Twist’s eyes, the pianist becomes a stand-in for the love-crazed composer in Berlioz’s original concept. Or as he put it: “He is the person having this fever dream.”

The object of his affections is represented by a ghostly white fabric. This is “hand-held Harriet,” named after Berlioz’s beloved, Harriet Smithson, whom the composer met and married three years after the symphony’s première. (Reader: It didn’t last.) The white apparition coincides with the first occurrence of a musical motif that returns many times. Berlioz called it his “idée fixe,” or obsession. Each time you hear the wistful melody, you see the fabric shape-shifting in the water. It feels vaguely human and abstract at the same time.

Until recently, this Harriet apparition was handled by Mr. Twist: “There were no strings or sticks or anything. The idea was to make it look like it was moving on its own. I had this feeling I was expressing myself through my hands and making this piece of cloth come to life.” He has since taught it to one of his puppeteers. He no longer performs in the show — at 48, he finds its physical demands more taxing than they once were. Now, he prefers to fine-tune the work of others.

A lot has happened in Mr. Twist’s career in the 20 years since the successful premiere of “Symphonie Fantastique.” His works have been shown at Lincoln Center (“Petrushka” and “The Rite of Spring”). He has created puppetry for several ballets (most notably works by Christopher Wheeldon) and on Broadway (“Charlie and the Chocolate Factory” and “The Addams Family”). He has directed operas. He helped design the Dementors, terrifying black ghouls in “Harry Potter and the Prisoner of Azkaban.” And in 2015 he won a MacArthur “genius” fellowship.

“Symphonie” was also the impetus behind Dream Music Puppetry program, a puppetry series that was inaugurated at HERE in 1998 with the premiere of the piece. The dedicated puppetry space downstairs, one of the few of its kind around the country, was founded with the help of a donation from his grandmother and still bears her name, Dorothy B. Williams. Her photograph sits outside the door. (This revival will be performed in the larger space upstairs.) Mr. Twist has been its artistic director since the beginning.

The city beyond HERE’s walls, though, has changed. “When I created ‘Symphonie’ I used to go down to Canal Street and get everything I needed — those stores are mostly gone now,” he said with a note of sadness. “You would touch things and feel materials instead of just ordering them online.”

All these years later, he’s still amazed that this assemblage of bits and pieces worked together as well as it did. Sometimes, he said, as he surveys the drenched props and the puddles on the floor, he wonders: “Wow, how did I do that?”